And I notice that while there ultimately is something extraordinary going on with Minuet, each time our heroes twig to it, they dismiss it as something which, while remarkable, could reasonably be accounted for by ordinary circumstances, as they initially believe that the Bynars have performed "nothing more" than an "enhancement" to correct the "problems" they had with the Holodeck in "The Big Goodbye"...
PICARD: Captain's log, stardate 41365.9... The Enterprise has been ordered to Starbase 74, in orbit around Tarsas III. A routine maintenance check of all systems will be made, and certain upgrades completed, including the Holodeck, with which we've had problems. I anticipate a glowing report. The ship has performed magnificently, beyond anyone's expectations.
[...]
RIKER: How much has been changed? What exactly did you do?
ONE ONE: Enhancement...
ZERO ZERO: ...nothing more.
[...]
PICARD: The sophistication of this programming is remarkable.
MINUET: In what way?
PICARD: The Holodeck has given us woodlands and ski slopes, figures that fight, and fictional characters with whom we can interact, but you...you're very different. You adapt. You spoke to me in French.
MINUET: It was very simple. When I heard your name, I merely accessed the foreign language bank.
PICARD: That's very impressive.
[...]
PICARD: She's so very different from the other images we've experienced on the Holodeck, isn't she? She's...she's more intuitive.
RIKER: It's as though she'd been plugged into my subconscious. She already knows what I want her to say before I'm aware of it myself.
PICARD: I suppose it's an understandable progression. Computers make decisions based on inputs, and we humans give off a multitude of subtle signs that...that communicate our emotions.
RIKER: It's uncanny. I could develop feelings for Minuet, exactly as I would for any woman.
PICARD: Doesn't love always begin that way, with the illusion more real than the woman?
[...]
RIKER: She's gone. I tried variations of the program, others appeared, but not Minuet.
PICARD: Maybe it was all part of the Bynars' programming. But you know, Number One, some relationships just can't work.
At the end there is even ostensibly some small hope/doubt left as to whether the Holodeck might have sustained Minuet on its own without the Bynars, and even after Riker repeatedly fails to reproduce her, Picard only gently suggests that "maybe" she owed her existence solely to their tinkering. (Though it was later reiterated in "Future Imperfect" that she was uniquely "part of a very special program" and ultimately persisted only as a fantasy in Riker's mind.) Essentially, it can be seen as a reset button being hit at the end of the episode, with the Holodeck having gained a little "something extra" temporarily (or did it?) and then lost it again (or did it?). We did later see sentience emerge in other holograms, so...there's that. I'll leave others to delve into the details further for now, and see what shakes out.